Item Summary

In this work, we focus on a subclass of channels with memory, called “channels with output memory”, in which the state of the channel is solely characterized by the previous output of the channel. This thesis contains two parts and covers modeling, signal processing and estimation problems in channels with output memory. In the first part, we model the multi- level per cell (MLC) flash channel, which has been widely used as the leading technology in non-volatile solid state drive (SSD) devices during the past decade, as a channel with output memory. We show that the state of an MLC flash channel at any given time depends only on the outputs of the neighboring cells due to the existing capacitance coupling effect. Our results on MLC flash channels mainly stem from the signal processing techniques in which we provide an accurate model for MLC flash memory ; using this model we find a mathematically tractable way to formulate the write process, and finally design the optimal detector for flash memory. The results can be summarized in four different groups : i) Modeling the MLC flash as a channel with output memory. ii) Obtaining a mathematical model to characterize the iterative write process using the renewal theory framework. iii) Obtaining the optimal step size in the iterative programming despite the trade-off between programming latency and accuracy. iv) Designing optimal soft/hard detectors for MLC flash memories.The second part of our work concentrates on parameter estimation for specific types of channels with output memory, which we call “Markov channels”, in which the channel in- put/output pairs form a Markov process. For this type of channel, we assume that there is no feedback and the input is a known i.i.d process, and we consider that both the set of contexts (channel states), and the transition probabilities (channel parameters) are unknown. We emphasize at the outset that we do not exclude slow mixing of the channel evolution. When a process has slow mixing property, a large number of observations is needed to explore the state space properly and the empirical properties of finite sized samples from Markov processes not necessarily reflect stationary properties. We observe a length-n sample of the input/output pair sequence generated by applying a known i.i.d input process and obtaining its corresponding output from an unknown, stationary ergodic Markov channel over a finite alphabet A. Using this sample, we want (i) a best approximation of the set of transition probabilities (ii) the stationary probabilities of an output string, and (iii) estimate or at least obtain heuristics of the information rate of the process. Two distinct problems that complicate estimation in this setting are long memory ; and slow mixing. Note that any consistent estimator can only converge pointwise over the class of all ergodic Markov models. But can we look at a length-n sample and identify if an estimate is likely to be accurate ? Since the memory is unknown a-priori, a natural approach is to estimate a potentially coarser model with memory kn = O(log n). As n grows, estimates get refined and this approach is consistent with the above scaling of kn, which is also known to be essentially optimal. However, the situation is vastly different when we want the best answers possible with a length-n sample. Combining the results of universal compression with the Aldous coupling arguments, we obtain sufficient conditions on the length-n sample (even for slow mixing models) to identify when naive (i) estimates of the model parameters are accurate ; (ii) estimates related to the stationary probabilities are accurate ; we also bound the deviations of the naive estimatesfrom the true values.

Description:

Ph.D. University of Hawaii at Manoa 2016.Includes bibliographical references.